Example 94.2 Iris Data

Fisher (1936)’s iris data give sepal and petal dimensions for three different species of iris. The data, which are available in the Sashelp library, are clustered by kth-nearest-neighbor density linkage by using the CLUSTER procedure with K=8. Observations are identified by species (Setosa, Versicolor, or Virginica) in the tree diagram, which is oriented with the height axis horizontal.


The following statements produce the results shown in Output 94.2.1 and Output 94.2.2:

title 'Fisher (1936) Iris Data';
ods graphics on;

proc cluster data=sashelp.iris method=twostage print=10 
             outtree=tree k=8 noeigen;
   var SepalLength SepalWidth PetalLength PetalWidth;
   copy Species;
run;
proc tree data=tree horizontal lineprinter pages=1 maxh=10;
   id species;
run;

The PAGES=1 option specifies that the tree diagram extend over one page from tree to root. Since the HORIZONTAL option is also specified, the horizontal extent of the diagram is one page. The number of vertical pages required for the diagram is dictated by the number of leaves in the tree.

The MAXH=10 limits the values displayed on the height axis to a maximum of 10. This prunes the tree diagram so that only the portion from the leaves to level 10 is displayed. You can see this pruning effect in Output 94.2.2.

Output 94.2.1 Clustering of Fisher’s Iris Data
Fisher (1936) Iris Data

The CLUSTER Procedure
Two-Stage Density Linkage Clustering


K = 8

Root-Mean-Square Total-Sample Standard Deviation 10.69224

Cluster History
Number
of
Clusters
  Freq Normalized
Fusion Density
Maximum Density
in Each Cluster
Tie
Clusters Joined Lesser Greater
10 CL11 OB79 48 0.2879 0.1479 8.3678  
9 CL13 OB112 46 0.2802 0.2005 3.5156  
8 CL10 OB113 49 0.2699 0.1372 8.3678  
7 CL8 OB91 50 0.2586 0.1372 8.3678  
6 CL9 OB120 47 0.1412 0.0832 3.5156  
5 CL6 OB118 48 0.107 0.0605 3.5156  
4 CL5 OB110 49 0.0969 0.0541 3.5156  
3 CL4 OB135 50 0.0715 0.0370 3.5156  
2 CL7 CL3 100 2.6277 3.5156 8.3678  


3 modal clusters have been formed.

Output 94.2.2 Horizontal Tree for Fisher’s Iris Data
Fisher (1936) Iris Data

The TREE Procedure
Two-Stage Density Linkage Clustering

                                   Cluster Fusion Density                       
                                                                                
                0     1     2     3     4     5     6     7     8     9    10   
                +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+   
  I      Setosa XXXXXXXXXXX..................................................   
  r             XXXXXXXXXXX                                                     
  i      Setosa XXXXXXXXXXXXXXXXXX...........................................   
  s             XXXXXXXXXXXXXXXXXX                                              
         Setosa XXXXXXXXXXXXXXXXXXXXX........................................   
  S             XXXXXXXXXXXXXXXXXXXXX                                           
  p      Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................   
  e             XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                  
  c      Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................   
  i             XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                 
  e      Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.............................   
  s             XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                               
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                           
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX    
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX     
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                               
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                 
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                  
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................   
                XXXXXXXXXXXXXXXXXXXXXXXX                                        
         Setosa XXXXXXXXXXXXXXXXXXXXXXXX.....................................   
                XXXXXXXXXXXXXXX                                                 
         Setosa XXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXX                                                   
         Setosa XXXXXXXXXXXXX................................................   
                XXXXXXXXXXXXX                                                   
         Setosa XXXXXXXXXXXXX................................................   
                XXXXXXXXXX                                                      
         Setosa XXXXXXXXXX...................................................   
                XXXXXXX                                                         
         Setosa XXXXXXX......................................................   
                XXXX                                                            
         Setosa XXXX.........................................................   
                XXX                                                             
         Setosa XXX..........................................................   
                                                                                
     Versicolor XXX..........................................................   
                XXX                                                             
     Versicolor XXX..........................................................   
                XXX                                                             
     Versicolor XXXXXXXX.....................................................   
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     Versicolor XXXXXXXXX....................................................   
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     Versicolor XXXXXXXXXXXXXXX..............................................   
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     Versicolor XXXXXXXXXXXXXXXXX............................................   
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     Versicolor XXXXXXXXXXXXXXXXX............................................   
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     Versicolor XXXXXXXXXXXXXXXXX............................................   
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     Versicolor XXXXXXXXXXXXXXXXXX...........................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXX.......................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXX......................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXX....................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXX....................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXX......................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXX.......................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXX.........................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXX.........................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXX.......................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                 
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                               
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.........................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                           
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX....................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                       
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.............   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.............   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                            
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.........................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXXX.......................................   
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     Versicolor XXXXXXXXXXXXXXXXXXXXX........................................   
                XXXXXXXXXXXXXXXXXXXX                                            
     Versicolor XXXXXXXXXXXXXXXXXXXX.........................................   
                XXXXXXXXXXXXXXXXXX                                              
     Versicolor XXXXXXXXXXXXXXXXXX...........................................   
                XXXXXXXXXXXXXXXXXX                                              
      Virginica XXXXXXXXXXXXXXXXXX...........................................   
                XXXXXXXXXXXXXXXX                                                
     Versicolor XXXXXXXXXXXXXXXX.............................................   
                XXXXXXXXXXXXXX                                                  
     Versicolor XXXXXXXXXXXXXX...............................................   
                XXXXXXXXXXXXX                                                   
     Versicolor XXXXXXXXXXXXX................................................   
                XXXXXXXXXXXX                                                    
     Versicolor XXXXXXXXXXXX.................................................   
                XXXXXXXXXXXX                                                    
     Versicolor XXXXXXXXXXXX.................................................   
                XXXXXXXXXX                                                      
      Virginica XXXXXXXXXX...................................................   
                XXXXXXX                                                         
     Versicolor XXXXXXX......................................................   
                XXX                                                             
     Versicolor XXX..........................................................   
                XXX                                                             
     Versicolor XXX..........................................................   
                XXX                                                             
      Virginica XXX..........................................................   
                X                                                               
      Virginica XX...........................................................   
                XX                                                              
      Virginica XX...........................................................   
                XX                                                              
      Virginica XXX..........................................................   
                XXX                                                             
      Virginica XXX..........................................................   
                XXX                                                             
      Virginica XXXX.........................................................   
                XXXX                                                            
     Versicolor XXXXX........................................................   
                XXXXX                                                           
      Virginica XXXXXX.......................................................   
                XXXXXX                                                          
      Virginica XXXXXX.......................................................   
                XXXXXX                                                          
      Virginica XXXXXXXXXX...................................................   
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      Virginica XXXXXXXXXXX..................................................   
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      Virginica XXXXXXXXXXX..................................................   
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      Virginica XXXXXXXXXXXX.................................................   
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      Virginica XXXXXXXXXXXXXX...............................................   
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      Virginica XXXXXXXXXXXXXX...............................................   
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      Virginica XXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXXXX                                                 
     Versicolor XXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXXXX                                                 
      Virginica XXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXXXX                                                 
      Virginica XXXXXXXXXXXXXXXX.............................................   
                XXXXXXXXXXXXXXXX                                                
      Virginica XXXXXXXXXXXXXXXX.............................................   
                XXXXXXXXXXXXXXXX                                                
     Versicolor XXXXXXXXXXXXXXXXXXX..........................................   
                XXXXXXXXXXXXXXXXXXX                                             
      Virginica XXXXXXXXXXXXXXXXXXX..........................................   
                XXXXXXXXXXXXXXXXXX                                              
      Virginica XXXXXXXXXXXXXXXXXX...........................................   
                XXXXXXXXXXXXXXXXXX                                              
      Virginica XXXXXXXXXXXXXXXXXX...........................................   
                XXXXXXXXXXXXXXXXX                                               
      Virginica XXXXXXXXXXXXXXXXXXX..........................................   
                XXXXXXXXXXXXXXXXXXX                                             
      Virginica XXXXXXXXXXXXXXXXXXXXX........................................   
                XXXXXXXXXXXXXXXXXXXXX                                           
      Virginica XXXXXXXXXXXXXXXXXXXXX........................................   
                XXXXXXXXXXXXXXXXXXXXX                                           
      Virginica XXXXXXXXXXXXXXXXXXXXX........................................   
                XXXXXXXXXXXXXXXXXXXX                                            
      Virginica XXXXXXXXXXXXXXXXXXXX.........................................   
                XXXXXXXXXXXXXXXXXXX                                             
      Virginica XXXXXXXXXXXXXXXXXXX..........................................   
                XXXXXXXXXXXXXXXXXX                                              
      Virginica XXXXXXXXXXXXXXXXXX...........................................   
                XXXXXXXXXXXXXXXX                                                
      Virginica XXXXXXXXXXXXXXXX.............................................   
                XXXXXXXXXXXXXXX                                                 
      Virginica XXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXXXX                                                 
      Virginica XXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXXX                                                  
      Virginica XXXXXXXXXXXXXX...............................................   
                XXXXXXXXXXXXXX                                                  
      Virginica XXXXXXXXXXXXXX...............................................   
                XXXXXXXXXXXXX                                                   
      Virginica XXXXXXXXXXXXX................................................   
                XXXXXXXXXXXXX                                                   
      Virginica XXXXXXXXXXXXX................................................   
                XXXXXXXXXXXX                                                    
      Virginica XXXXXXXXXXXX.................................................   
                XXXXXXXXXXX                                                     
      Virginica XXXXXXXXXXX..................................................   
                XXXXXXXX                                                        
      Virginica XXXXXXXX.....................................................   
                XXXXXXXX                                                        
      Virginica XXXXXXXX.....................................................   
                XXXXXX                                                          
      Virginica XXXXXX.......................................................   
                XXXXXX                                                          
      Virginica XXXXXX.......................................................   
                XXXXX                                                           
      Virginica XXXXX........................................................   
                XXXXX                                                           
      Virginica XXXXX........................................................   
                XXXX                                                            
      Virginica XXXX.........................................................   
                XXXX                                                            
      Virginica XXXX.........................................................   
                XXX                                                             
      Virginica XXX..........................................................   
                XX                                                              
      Virginica XX...........................................................   
                X                                                               
      Virginica X............................................................